What is the function of Air pressure switch in a compressor?

Shuts off the compressor when it reaches the set point. Hope this wasn't homework, we do not answer those questions.

It depends some on the compressor. Some smaller units it actually turns the motor off & on as need to maintain pressure setting. In many larger units it indirectly closes the cylinder exhaust valves so the cylinders create compression and then releases the valves so there is no compression when pressure is reached, but the motor stays running. It is referred to as loading and unloading. In a multi-stage compressor you can actually hear the stages load or unload(valves in that stage closing or opening) I have worked on units that have multiple stages and the pressure switch itself has multiple stages to control the valves when the stages are needed or not needed.